Adaptive machining

ABSTRACT

Methods and apparatus for adaptively controlling a machine tool to provide optimized instantaneous performance as unforeseen or unforeseeable changes in cutting conditions occur; -characterized by a continuous search out of and back into a permissible area defined by constraint boundaries in the cutter speed vs. feed rate (V vs. R) plane. The method and apparatus always adjust the cutter speed and feed rate to conditions of optimized economic operation (e.g., minimum cost or minimum time)-but subject to other limitations of the machine tool, the cutter and the workpiece material-because one such boundary defines the optimum values of cutter speeds and feeds representing minimum cost or minimum time per unit length of machining. The latter boundary is established by straightforward use of empirical contants, available in the literature or readily determined by known techniques, associated with the well known modified Taylor equation. By sensing machine tool variable and signaling actual values of a plurality of operating parameters, the output rate of the machine tool is increased until the economic restraint, or some other inherent limitation restraint, is reached. The corrective action to remove any constraint violation is based upon a grouping of the several signaled parameters according to the shapes of the respective boundary lines corresponding thereto in the V, R plane, so that the method steps for effecting correction of any constraint boundary violation are relatively few in number and may be carried out by novel apparatus which is simple and practical.

eadie et all.

were

Jan. 8, 197 1 1 1 ADAPTIVE MACK-11111116 [75] Inventors: Bruce R. Beadle, Fond du Lac; John G. Bollinger, Madison, both of Wis.

[73] Assignee: Giddings & Lewis, line, Ford du Lac, Wis.

[22] Filed: July 3, 1972 [21] Appl. No.1 268,648

[30] Foreign Application Priority Data Nov. 9, 1971 Great Britain 51917/71 [52] 11.5. C1.... 235/151.1]l, 235/150.1 [51] int. Cl G051) 13/02, G06f 15/46 [58] Fieid of Search 235/15l.1l, 150.1

[56] References Cited UNlTED STATES PATENTS 2,980,330 4/1961 Ablow et a1. 235/1501 3,548,172 12/1970 Centner et a1... 235/l5l.l1 3,634,664 1/1972 Valek 235/l5l.11 3,665,493 5/1972 Glowzewski 235/l5l.l1

Primary Examiner-Eugene G. Botz Attorney-Wolfe, Hubbard, Leydig, Voit & Osann [57] ABSTRACT Methods and apparatus for adaptively controlling a machine tool to provide optimized instantaneous performance as unforeseen or unforeseeable changes in cutting conditions occur; characterized by a continuous search out of and back into a permissible area defined by constraint boundaries in the cutter speed vs. feed rate (V vs. R) plane. The method and apparatus always adjust the cutter speed and feed rate to conditions of optimized economic operation (e.g., minimum cost or minimum time)but subject to other limitations of the machine tool, the cutter and the workpiece material-because one such boundary defines the optimum values of cutter speeds and feeds representing minimum cost or minimum time per unit length of machining. The latter boundary is established by straightforward use of empirical contants, available in the literature or readily determined by known techniques, associated with the well known modified Taylor equation. By sensing machine tool variable and signaling actual values of a plurality of operating parameters, the output rate of the machine tool is increased until the economic restraint, or some other inherent limitation restraint, is reached. The corrective action to remove any constraint violation is based upon a grouping of the several signaled parameters according to the shapes of the respective boundary lines corresponding thereto in the V, R plane, so that the method steps for effecting correction of any constraint boundary violation are relatively few in number and may be carried out by novel apparatus which is simple and practical.

41 Claims, 85 Drawing Figures PATENTED JAN 8 I974 3.784.798 sum 18 0F 53 mvm .azi 

1. The method of machining a workpiece in a machine tool having a cutter rotatable at a controllable speed V and having means to bodily move the cutter at a controllable feed rate R relative to the workpiece, said method comprising a. signaling from variables sensed at the machine tool a plurality of actual values of operating parameters while the cutter is operatively acting on the workpiece with existing values of speed V and rate R, b. signaling predetermined limit values of parameter constraint boundaries which define a permissible operating region within the V, R plane, (b1) at least one of said limit values representing a constraint boundary beyond which the economic performance of the machining operation is unacceptably degraded, c. utilizing said signaled actual and limit values to determine if the then existing values of speed V and rate R define a point in the V, R plane which lies outside said region, d. in response to such determination, changing the one or both of the speed V and rate R values in a sense to restore the V, R operating point to wiThin said region, and e. in the absence of such determination, increasing one of the speed V and rate R values.
 2. The method set forth in claim 1, further characterized in that said step (d) comprises (d1) in response to a determination that a constraint boundary, which in the V, R plane is a line of generally positive slope, is violated, increasing speed V and decreasing rate R, and (d2) in response to a determination that a constraint boundary, which in the V, R plane is a line of generally negative or infinite slope, is violated, decreasing both speed V and rate R.
 3. The method set forth in claim 1, further characterized in that said at least one limit value named at (b1) is a constant K1 derived from economic relationships and which represents the limit of the quantity Vfq as the speed V and rate R take on different values; q being a predetermined constant and f representing feed per tooth.
 4. The method set forth in claim 1, further characterized in that said sensed variables are selected from the group consisting of speed V, rate R, deflection dy normal to the direction of cutting, deflection dx parallel to the direction of cutting, torque T exerted to rotate the cutter and workpiece relative to each other, and vibration U of the cutter.
 5. The method set forth in claim 4, further characterized in that said signaled actual values represent operating parameters selected from the group consisting of chipload f, deflection dy, deflection dx, torque T, power P, feed rate R, vibration U, the modified Taylor quantity Vfq and speed V.
 6. The method set forth in claim 1, further characterized in that said signaled limit values represent parameters selected from the group consisting of maximum chipload (fmax), maximum deflection (dy ) normal to direction of feed, maximum deflection (dx ) parallel to direction of feed, maximum torque (Tmax), maximum power (Pmax), maximum feed rate (Rmax), maximum cutter vibration (Umax), minimum cost or minimum time per unit length of cutting (Vfqmax), minimum chipload (fmin), maximum speed (Vmax), and minimum speed (Vmin).
 7. The method of machining a workpiece in a machine tool having a cutter rotatable at a controllable speed V and translatable at a controllable feed rate R relative to the workpiece, said method comprising a. signaling the actual values of selected operating parameters of the machine tool while the cutter is operatively acting on the workpiece with existing values of speed V and rate R, b. signaling the limit values of a plurality of parameters which define constraint boundaries of a satisfactory operating region in the V, R plane, where at least one of said constraint boundaries represents the locus of the values of speed V and rate R which will result in substantially optimized cost or time for machining a unit length along the workpiece, c. measuring off successive iterating time periods of short duration while machining is in progress, d. signaling during each time period whether the signaled actual value exceeds the signaled limit value with respect to one or more of said parameters, e. in response to such signaling, correctively changing the value of either or both the feed rate R and the speed V by an incremental amount and in a direction tending to restore the excessive actual value back toward equality with the limit value, and f. in the absence of such signaling during any of said time periods, increasing the value of the feed rate R by a predetermined incremental amount.
 8. The method set forth in claim 7 further characterized in that the signaling of said limit value of said one constraint, as recited in phrase (b), in the signaling of a constant K1; one of the siGnaled actual values of operating parameters is Vfq where V is cutter speed, f is chipload and q is a constant associated with the modified Taylor equation; and said value Vfq is compared with said constant K1 to determine when the former exceeds the latter.
 9. The method set forth in claim 7 wherein the signaled actual values of operating parameters are selected from the group consisting of speed V, rate R, chipload f, deflections dy and dx, torque T, power P, vibration U, and specifically includes the value Vfq where q is an exponent in the applicable modified Taylor equation.
 10. The combination set forth in claim 9 wherein the signaled limit values are all constants which are empirically or experimentally determined and represent limit values of variables selected from the group consisting of maximum and minimum chipload, maximum and minimum speed V, maximum deflections dy and dx, maximum torque T, maximum power P, maximum feed rate R, maximum vibration U, and maximum Vfq.
 11. In a system for controlling a machine tool having means for rotating a cutter and moving it bodily relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, the combination comprising a. means for sensing variables at the machine tool and dynamically signaling from such variables the actual values of a plurality of operating parameters while the cutter is acting on the workpiece with existing values of speed V and rate R, means for signaling limit values of a plurality of parameters which define constraint boundaries defining a satisfactory operating region in the V, R plane, and wherein one of said constraint boundaries defines the locus of conjoint values of speed V and rate R which will result in substantially minimum cost or minimum time for per unit length machined along the workpiece, c. means for comparing parameter actual value signals with the respective ones of said limit value signals to produce violation signals indicative of the fact when any actual value violates the limit value, d. means responsive to said violation signals for changing either or both speed V or rate R in a sense to remove the violation, and e. means responsive to the absence of any violation signal for increasing the feed rate R.
 12. The combination set forth in claim 11, further characterized in that said one constraint boundary lies along the line Vfq K1 in the V, R plane, where f represents chipload, q is a constant from the applicable modified Taylor equation, and K1 is a constant having a value determined from economic relationships.
 13. The combination set forth in claim 12, further characterized in that said constant K1 is proportional to the quantity (1/T)n, where T is the tool life and n is one of the exponents in the modified Taylor equation VTnfq K.
 14. The combination set forth in claim 12 wherein the constant K1 is equal to (n M1/(1-n) M2)n where n and q are the constants in the applicable modified Taylor equation VTnfq K and the constants M1 and M2 are derived from economic and Taylor relationships.
 15. The combination set forth in claim 11 further characterized in that said means (a) includes means for sensing variables selected from the group consisting of speed V, rate R, deflections dx and dy, torque T and vibration U.
 16. The combination set forth in claim 11, further characterized in that the operating parameters for which actual values are signaled are selected from the group consisting of chipload f, deflections dy and dx, torque T, power P, feed rate R, vibration U, the modified Taylor quantity Vfq, and the speed V.
 17. The combination set forth in claim 16, further characterized in that said signaled limit values include limits selected from the group consisting of maximum chipload (fmax), maximum deflections (dy and dx ), maximum torque (Tmax), maximum power (Pmax), maximum feed rate (Rmax), maximum vibration (Umax), maximum value of the function Vfqmax), minimum chipload (fmin), maximum speed (Vmax) and minimum speed (Vmin).
 18. In a system for controlling a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and feed rate R, the combination comprising a. means for measuring off successive short time intervals, b. means for sensing a plurality of operational variables at the machine tool while the cutter is operatively acting upon the workpiece and signaling during each time interval the then existing actual values of a plurality of operating parameters one of which is a conjoint function of the speed V and chipload f, c. means for signaling a plurality of limit values for said parameters and which define a plurality of boundary constraints bounding an area in the V, R plane for permissible operation, d. means for comparing the actual value signals with the corresponding limit value signals during each time interval to produce violation signals in each case where the actual value of a parameter falls outside its boundary constraint, e. means responsive to any violation signal during any time interval for changing during the time interval one or both of speed V and rate R in a sense to lessen the violation, and f. means responsive to the absence of any violation signal during any time interval for increasing the feed rate R by a predetermined increment.
 19. The combination set forth in claim 18 further characterized in that said conjoint function is Vfq, where q is a constant from the applicable modified Taylor equation.
 20. The combination set forth in claim 18 further characterized in that the said conjoint function parameter is compared by said means (d) with a corresponding limit value K1, where K1 is a constant derived from economic factors and constants from the applicable modified Taylor equation.
 21. The combination set forther in claim 20 further characterized in that K1 is equal to K ((RL + ROH)/CT . n/1-n)n where K and n are constants from the applicable modified Taylor equation VTnfq K, RL and ROH are the labor and overhead cost rates for operation of the machine tool, and CT is the cost associated with changing of the cutter in the machine tool.
 22. The combination set forth in claim 18 further characterized in that said means (e) includes means, responsive to violation of a constraint boundary which in the V, R plane is of generally positive slope, for incrementally increasing V and decreasing R; and means responsive to violation of a constraint boundary which in the V, R plane is of generally negative or infinite slope, for incrementally decreasing V and decreasing R.
 23. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, said method comprising a. sensing operating variables at the machine tool and signaling the actual values of a plurality of operating parameters while the cutter is operative upon the workpiece, b. signaling the limit values of a first plurality (Class I) of operating parameters, each such parameter having values of V and R, when the limit is reached, which reside on a line of Generally positive slope in the V, R plane, c. signaling the limit values of a second plurality (Class II) of operating parameters, each such parameter having values of V and R, when the limit is reached, which reside on a line of generally negative or infinite slope in the V, R plane, d. comparing the signaled actual values with the corresponding ones of said limit values for said first plurality of operating parameters and producing a first control signal when any one or more of such actual values exceeds the corresponding limit value, e. comparing the signaled actual values for said second plurality of operating parameters and producing a second control signal when any one or more of such actual values exceeds the corresponding limit value, f. decreasing said feed rate R in response to either the first or second control signal, g. decreasing said speed V in response to said second control signal, h. increasing said speed V in response to said first control signal and the absence of said second control signal, and i. increasing said feed rate R in the absence of both said first and second control signals.
 24. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, said method comprising a. sensing operating variables at the machine tool and signaling the actual values of a plurality of operating parameters while the cutter is operative upon the workpiece; b. signaling the limit values of a first plurality (Class I) of operating parameters which vary with V and R such that the values of V and R lie, when the limit is reached, along lines in the V, R plane representable by the equation AV f A1V( )R 1 where A, A1, Alpha , Beta are constants unique to each parameter but such that Alpha >0 and Beta / Alpha << 1 for all the parameters, c. signaling the limit values of a second plurality of operating parameters which vary with V and R such that the values of V and R lie, when the limit is reached, along lines in the V, R plane representable by the equation A V f A1V( ) R 1 where A, A1, Alpha , Beta are constants unique to each parameter but such that Alpha >0 and Beta > or = Alpha for all the parameters, d. decreasing the rate R when any signaled actual value exceeds the corresponding signaled limit value of any of the first or second pluralities of parameters, e. decreasing said speed V when any signaled actual value exceeds the corresponding signaled limit value of any parameter in said second plurality but only if no signaled actual value exceeds the corresponding limit value for a parameter in said first plurality, f. increasing said speed V when any signaled actual value exceeds the corresponding signaled limit value of any parameter in said first plurality but only if no signaled actual value exceeds the corresponding limit value for a parameter in said second plurality, and g. increasing said rate R when none of said signaled actual values exceeds the corresponding signaled limit value.
 25. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, said method comprising a. sensing a plurality of variables at the machine tool and signaling the actual values of a plurality of operating parameters, b. said parameters having ascertainable limit values which due to machine tool capabilities or work quality standards or production economics desirably are not to be violated, c. the locus of the V and R values in the V, R plane when each of said parameters is at its liMit value being representable by a boundary line of the family A V f A1V( )R 1, where A, A1, Beta and Alpha are constants unique to each line corresponding to each of said parameters, said lines falling into a Class I having generally positive slopes, a Class II having generally negative or infinite slopes, and a Class III representing lower and upper bounds with zero slopes, d. signaling said limit values for each of said parameters, e. comparing the limit signals with the corresponding actual value signals to produce a violation signal in any case where the limit is violated, f. increasing or decreasing the speed V to eliminate the violation in response to any violation of a Class III restraint, g. decreasing the speed V and decreasing the rate R in response to any signaled violation of a Class II restraint unaccompanied by a signaled violation of a Class III or Class I restraint, h. increasing the speed V and decreasing the rate R in response to a signaled violation of any Class I restraint unaccompanied by violation of a Class II or Class III restraint, an i. increasing the rate R in response to the absence of all violation signals.
 26. The combination set forth in claim 23 further characterized in that one of said first plurality of parameters is Vfq where f is the chipload of the cutter and q is a constant from the applicable modified Taylor equation.
 27. The combination set forth in claim 26 further characterized in that the limit value of said one parameter is a constant equal to K/Tn where K and n are constants and T is useful cutter life in the applicable modified Taylor equation VTnfq K.
 28. The combination set forth in claim 26 further characterized in that the limit value of said one parameter is a constant K1 equal to K (n (RL + ROH)/(1-n) CT)n where K and n are constants from the applicable modifier Taylor equation, CT is the cost of a tool change, and RL and ROH are the labor and overhead cost rates for operation of the machine tool.
 29. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, said method comprising a. sensing operating variables at the machine tool and signaling the actual values of a plurality of operating parameters while the cutter is operative upon the workpiece, b. signaling the limit values of a first plurality (Class I) of operating parameters, each such parameter having values of V and R, when the limit is reached, which reside on lines represented in the V, R plane by the equation A1 V( )R 1 where A1, Beta and Alpha are constants unique to each such parameter and where for all such parameters Alpha >0 and Beta Alpha <<1, c. signaling the limit values of a second plurality (Class II) of operating parameters having values of V and R which reside, when the limit is reached on lines as aforesaid but where for all such parameters Alpha > 0, and Beta > or = Alpha , d. signaling the limit values of two (Class III) operating parameters having values of V and R which reside, when the limit is reached, on lines as aforesaid but where for all such parameters Beta 0 and Beta 1 ; e. reducing the speed V when i. the higher one of said two signaled limit values for Class III parameters is exceeded by the corresponding signaled actual value, or ii. any one of said signaled Class II limit values is exceeded by the corresponding signaled actual value while none of thE signaled Class I limit values is exceeded by the corresponding signaled actual value; f. increasing the speed V when i. the lower one of said two signaled limit values for Class III parameters is greater than the corresponding signaled actual value, or ii. any one of said Class I signaled limit values is exceeded by the corresponding signaled actual values, while none of the Class II signaled limit values is exceeded by the corresponding signaled actual value; g. decreasing the feed rate R when i. any one of the Class I or Class II signaled limit values is exceeded by the corresponding signaled actual value; and h. increasing the feed rate R when the condition recited at (g) (i) above does not exist.
 30. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and at a controllable feed rate R, said method comprising a. sensing a plurality of operating variables at the machine tool and signaling actual values of a plurality of parameters which the cutter is operative on the workpiece, b. signaling the limit values of a first plurality (Class I) of operating parameters having values of V and R which, when the limit is reached, lie along lines representable in the V, R plane by the general equation A1V( ) R 1 where A1 is a constant unique to each such parameter and Alpha Beta constants which may differ for the different parameters but which in all cases Alpha >0 and Beta Alpha <<1, c. signaling the limit values of a second plurality (Class II) of operating parameters having values of V and R where, when the limit is reached, lie along lines representable in the V, R plane by said equation, but for which Alpha >0 and Beta > or = Alpha ; d. measuring off successive equal short time periods; e. decreasing the existing feed rate R by a predetermined increment Delta R1 during each time period when any of said signaled limits is exceeded by the corresponding signaled actual value; f. decreasing the speed V by a predetermined increment Delta V1 during each time period when any of said Class II limits is exceeded by the corresponding signaled actual value; g. increasing the speed V by a predetermined increment Delta V2 during each time period when any of said Class I limits is exceeded by the corresponding signaled actual value; and h. increasing the feed rate R by a predetermined increment Delta R2 during each time period when the decreasing recited at (e) above is not effected.
 31. The method of machining a workpiece in a machine tool having a cutter rotatable and bodily movable relative to a workpiece respectively at a controllable speed V and a controllable feed rate R, said method comprising a. sensing certain operating variables at the machine tool and signaling the actual values of a plurality of parameters while the cutter is operative on the workpiece, said parameters including at least the modified Taylor equation quantity Vfq and one other parameter Pa which is desirably constrained during operation of the machine tool, b. said parameter Pa being representable in the V, R plane when the constraint limit is reached by a line corresponding to the equation AV f A1V( )R 1 where A and A1 are predetermined constants and Alpha and Beta are constants whose magnitudes and relative magnitudes are only generally known, c. signaling limit values for the parameters Vfq and Pa; d. decreasing the speed V and decreasing the feed rate R whenever the Vfq actual value signal exceeds the Vfq limit value signal, e. correctively chaNging the speed V and/or rate R whenever the Pa actual value signal exceeds the Pa limit value signal, and f. increasing the rate R when neither the Vfq nor Pa actual value signals exceed their corresponding limit values.
 32. The method set forth in claim 31 wherein the limit value of the Vfq parameter is a constant substantially equal to K1 (n( Alpha - Beta ) (RL + ROH)/CT( Alpha - Beta q + n ( Beta - Alpha ))n where RL and ROH are the labor and overhead cost rates for operation of the machine too; CT is the cost of a tool change; K, q and n are the constants for the applicable modified Taylor equation and Alpha and Beta are constants empirically and intuitively determined as applicable in the aforesaid equation AV Beta f Alpha 1 as defining the limit of the parameter Pa.
 33. The method set forth in claim 31 further characterized in that the signaled limit value of the parameter Vfq is numerically equal to K (n (RL + ROH)/(1-n) CT)n where RL and ROH are the labor and overhead cost rates for operation of the machine tool; CT is the cost of a tool change, K and n are constants for the applicable modified Taylor equation; and also characterized in that the constraint limit for the operating parameter Pa is defined by the aforesaid equation AV f 1 when Beta is approximately zero and Alpha is approximately
 1. 34. The method set forth in claim 31 further characterized in that the signaled limit value of the parameter Vfq is numerically proportional to 1/Tn where T is a specified, desired tool life and n is a constant from the applicable modified Taylor equation.
 35. The method of machining a workpiece in a machine tool having a cutter rotatable at a controllable speed and having means to bodily move the cutter at a controllable feed rate relative to the workpiece, said method comprising sensing the values of selected operating parameters of the machine tool while the cutter is operatively acting on the workpiece with existing values of speed and feed rate, deriving from said sensed values signals representing a plurality of constraints in the feed versus speed plane which represent boundary limits upon operation of the machine tool, at least one of said constraints representing a boundary of feeds and speeds required for operation with an optimized economic (e.g., minimum cost per part or minimum time per part) performance, measuring off successive iterating time periods of short duration, signaling during each time period whether the actual values of cutter speed and feed rate define a point in the speed versus feed plane which violates the boundary represented by each of the signaled constraints, correctively changing the existing value of the cutter speed or feed by an incremental amount in the direction to eliminate the violation in response to signaling that said point violates at least one boundary during any of said time periods, and increasing said feed rate by an incremental amount in response to signaling that said point does not violate any boundary during any of said time periods.
 36. The method set forth in claim 35 further characterized in that when two boundary violations are signaled during the same time period and the corrective actions to eliminate such two violations involved respectively increasing and decreasing the spindle speed, making no incremental change in speed during that time period.
 37. The method set forth in claim 35 further characterized in that when two boundary violations are signaled during the same time period and the respective corrective actions therefore are in the same Direction upon speed or feed, making a single incremental corrective change in the speed or feed.
 38. The method set forth in claim 35 further characterized in that said constraint representing a boundary for opitmized economic performance is of the nature Vfq < or = (n/1-n . M1/M2)n where V represents cutter speed f represents chipload q represents an empirically determined exponent n represents a predetermined constant M1 and M2 represent cost coefficients.
 39. The method set forth in claim 35 wherein at least one of said constraints is of the type exemplified by ''''maximum power'''' and the corrective action taken in response to a signaled violation of the constraint boundary is to incrementally decrease both the cutter speed and feed rate.
 40. The method set forth in claim 35 wherein at least one of said constraints is of the type exemplified by ''''maximum chipload'''' and the corrective action taken in response to a signaled violation is to incrementally increase cutter speed and incrementally decrease feed rate.
 41. The method set forth in claim 35 wherein at least one of said constraints is of the type exemplified by a machine parameter limit (such as maximum cutter speed), and the corrective action taken in response to a signaled violation is to incrementally change the parameter value in a direction to restore it to the limit value. 